Southwest Native Americans Knew Advanced Geometry

Researchers from Arizona State University (ASU) have found that the Southwest Native Americans had advanced geometry skills that enabled them to build sophisticated architectural complexes. They were so good in fact, they could be called Pythagoreans.

These findings represent the first potential quantitative evidence of knowledge of advanced geometrical constructs in a prehistoric North American society, which is particularly remarkable given that the ancestral Pueblo peoples had no written language or number system.

The researchers found apparent evidence that the ancestral Pueblo peoples laid out the site using the Golden rectangle, Pythagorean 3:4:5 triangles, equilateral triangles, and 45° right triangles.

The geometrical shapes used within this location would be familiar to any high school student: equilateral triangles, squares, 45-degree right triangles, Pythagorean triangles, and the "Golden rectangle," which was well known to architects in ancient Greece and Egypt and is often used in Western art due to its pleasing proportions.

With some geometrical know-how, a straight-edge, a compass or cord, and a unit of measurement, all of the shapes are fairly easy to construct. But, unlike the ancient Greeks, Egyptians and Maya, the ancestral Pueblo people had no written language or number system to aid them when they built the site. Incredibly, their measurements were still near-perfect, with a relative error of less than one percent.

The survey also revealed that a single unit of measurement, L = 30.5 ± 0.5 cm, or one third of that, appeared to be associated with many key features of the site. Further study is needed to determine if this unit of measurement is common to other ancestral Pueblo sites, and also if geometric constructs are apparent at other sites.

Dr. Sherry Towers, ASU Professor at the Simon A. Levin Mathematical, Computational and Modeling Sciences Center has spent many years studying the Sun Temple archaeological site in Mesa Verde National Park in Colorado, constructed around A.D. 1200.

Dr. Towers had said, "The site is known to have been an important focus of ceremony in the region for the ancestral Pueblo peoples, including solstice observations. My original interest in the site involved looking at whether it was used for observing stars as well."

Towers further stated, "I noticed in my site survey that the same measurements kept popping up over and over again. When I saw that the layout of the site's key features also involved many geometrical shapes, I decided to take a closer look."

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